Resilience of the Spectral Standard Model

We show that the inconsistency between the spectral Standard Model and the experimental value of the Higgs mass is resolved by the presence of a real scalar field strongly coupled to the Higgs field. This scalar field was already present in the spectral model and we wrongly neglected it in our previous computations. It was shown recently by several authors, independently of the spectral approach, that such a strongly coupled scalar field stabilizes the Standard Model up to unification scale in spite of the low value of the Higgs mass. In this letter we show that the noncommutative neutral singlet modifies substantially the RG analysis, invalidates our previous prediction of Higgs mass in the range 160--180 Gev, and restores the consistency of the noncommutative geometric model with the low Higgs mass.Comment: 13 pages, more contours added to Higgs mass plot, one reference adde

Higgs and Dark Matter Hints of an Oasis in the Desert

Recent LHC results suggest a standard model (SM)-like Higgs boson in the vicinity of 125 GeV with no clear indications yet of physics beyond the SM. At the same time, the SM is incomplete, since additional dynamics are required to accommodate cosmological dark matter (DM). In this paper we show that interactions between weak scale DM and the Higgs which are strong enough to yield a thermal relic abundance consistent with observation can easily destabilize the electroweak vacuum or drive the theory into a non-perturbative regime at a low scale. As a consequence, new physics--beyond the DM itself--must enter at a cutoff well below the Planck scale and in some cases as low as O(10 - 1000 TeV), a range relevant to indirect probes of flavor and CP violation. In addition, this cutoff is correlated with the DM mass and scattering cross-section in a parameter space which will be probed experimentally in the near term. Specifically, we consider the SM plus additional spin 0 or 1/2 states with singlet, triplet, or doublet electroweak quantum numbers and quartic or Yukawa couplings to the Higgs boson. We derive explicit expressions for the full two-loop RGEs and one-loop threshold corrections for these theories.Comment: 29 pages, 13 figure

Implications of the 125 GeV Higgs boson for scalar dark matter and for the CMSSM phenomenology

We study phenomenological implications of the ATLAS and CMS hint of a $125\pm 1$ GeV Higgs boson for the singlet, and singlet plus doublet non-supersymmetric dark matter models, and for the phenomenology of the CMSSM. We show that in scalar dark matter models the vacuum stability bound on Higgs boson mass is lower than in the standard model and the 125 GeV Higgs boson is consistent with the models being valid up the GUT or Planck scale. We perform a detailed study of the full CMSSM parameter space keeping the Higgs boson mass fixed to $125\pm 1$ GeV, and study in detail the freeze-out processes that imply the observed amount of dark matter. After imposing all phenomenological constraints except for the muon $(g-2)_\mu,$ we show that the CMSSM parameter space is divided into well separated regions with distinctive but in general heavy sparticle mass spectra. Imposing the $(g-2)_\mu$ constraint introduces severe tension between the high SUSY scale and the experimental measurements -- only the slepton co-annihilation region survives with potentially testable sparticle masses at the LHC. In the latter case the spin-independent DM-nucleon scattering cross section is predicted to be below detectable limit at the XENON100 but might be of measurable magnitude in the general case of light dark matter with large bino-higgsino mixing and unobservably large scalar masses.Comment: 17 pages, 7 figures. v3: same as published versio

Vacuum Stability, Perturbativity, and Scalar Singlet Dark Matter

We analyze the one-loop vacuum stability and perturbativity bounds on a singlet extension of the Standard Model (SM) scalar sector containing a scalar dark matter candidate. We show that the presence of the singlet-doublet quartic interaction relaxes the vacuum stability lower bound on the SM Higgs mass as a function of the cutoff and lowers the corresponding upper bound based on perturbativity considerations. We also find that vacuum stability requirements may place a lower bound on the singlet dark matter mass for given singlet quartic self coupling, leading to restrictions on the parameter space consistent with the observed relic density. We argue that discovery of a light singlet scalar dark matter particle could provide indirect information on the singlet quartic self-coupling.Comment: 25 pages, 10 figures; v2 - fixed minor typos; v3 - added to text discussions of other references, changed coloring of figures for easier black and white viewin

Multi-Scalar-Singlet Extension of the Standard Model - the Case for Dark Matter and an Invisible Higgs Boson

We consider a simple extension of the Standard Model by the addition of N real scalar gauge singlets \vp that are candidates for Dark Matter. By collecting theoretical and experimental constraints we determine the space of allowed parameters of the model. The possibility of ameliorating the little hierarchy problem within the multi-singlet model is discussed. The Spergel-Steinhardt solution of the Dark Matter density cusp problem is revisited. It is shown that fitting the recent CRESST-II data for Dark Matter nucleus scattering implies that the standard Higgs boson decays predominantly into pairs of Dark Matter scalars. It that case discovery of the Higgs boson at LHC and Tevatron is impossible. The most likely mass of the dark scalars is in the range 15 GeV \lsim \mvp \lsim 50 GeV with BR(h \to \vp\vp) up to 96%.Comment: 18 pages, 15 figure

Vacuum stability, neutrinos, and dark matter

Motivated by the discovery hint of the Standard Model (SM) Higgs mass around 125 GeV at the LHC, we study the vacuum stability and perturbativity bounds on Higgs scalar of the SM extensions including neutrinos and dark matter (DM). Guided by the SM gauge symmetry and the minimal changes in the SM Higgs potential we consider two extensions of neutrino sector (Type-I and Type-III seesaw mechanisms) and DM sector (a real scalar singlet (darkon) and minimal dark matter (MDM)) respectively. The darkon contributes positively to the $\beta$ function of the Higgs quartic coupling $\lambda$ and can stabilize the SM vacuum up to high scale. Similar to the top quark in the SM we find the cause of instability is sensitive to the size of new Yukawa couplings between heavy neutrinos and Higgs boson, namely, the scale of seesaw mechanism. MDM and Type-III seesaw fermion triplet, two nontrivial representations of $SU(2)_{L}$ group, will bring the additional positive contributions to the gauge coupling $g_{2}$ renormalization group (RG) evolution and would also help to stabilize the electroweak vacuum up to high scale.Comment: 18 pages, 15 figures; published versio

A survey of spectral models of gravity coupled to matter

This is a survey of the historical development of the Spectral Standard Model and beyond, starting with the ground breaking paper of Alain Connes in 1988 where he observed that there is a link between Higgs fields and finite noncommutative spaces. We present the important contributions that helped in the search and identification of the noncommutative space that characterizes the fine structure of space-time. The nature and properties of the noncommutative space are arrived at by independent routes and show the uniqueness of the Spectral Standard Model at low energies and the Pati-Salam unification model at high energies.Comment: An appendix is added to include scalar potential analysis for a Pati-Salam model. 58 Page

Sterile neutrino portal to Dark Matter II: exact dark symmetry

We analyze a simple extension of the standard model (SM) with a dark sector composed of a scalar and a fermion, both singlets under the SM gauge group but charged under a dark sector symmetry group. Sterile neutrinos, which are singlets under both groups, mediate the interactions between the dark sector and the SM particles, and generate masses for the active neutrinos via the seesaw mechanism. We explore the parameter space region where the observed Dark Matter relic abundance is determined by the annihilation into sterile neutrinos, both for fermion and scalar Dark Matter particles. The scalar Dark Matter case provides an interesting alternative to the usual Higgs portal scenario. We also study the constraints from direct Dark Matter searches and the prospects for indirect detection via sterile neutrino decays to leptons, which may be able to rule out Dark Matter masses below and around 100 GeV

Rν\nuMDM and Lepton Flavor Violation

A model relating radiative seesaw and minimal dark matter mass scales without beyond the standard model (SM) gauge symmetry (R$\nu$MDM) is constructed. In addition to the SM particles, the R$\nu$MDM contains, a Majorana fermion multiplet $N_R$ and scalar multiplet $\chi$ that transform respectively as $(1,5,0)$ and $(1,6,-1/2)$ under the SM gauge group $SU(3)_C\times SU(2)_L\times U(1)_Y$. The neutral component $N_R^0$ plays the role of dark matter with a mass in the range of 9 to 10 TeV. This scale also sets the lower limit for the scale for the heavy degrees of freedom in $N_R$ and $\chi$ which generate light neutrino masses through the radiative seesaw mechanism. The model predicts an $N_R^0$-nucleus scattering cross section that would be accessible with future dark matter direct detection searches as well as observable effects in present and searches for charged lepton flavor violating processes, such as $l_i\to l_j \gamma$ and $\mu - e$ conversion.Comment: Latex 18 pages with 7 figures. Discussions added in dark matter section and a few references adde